Abstract:

The field of this disclosure is making three-dimensional topographic
structures by means of graduated exposure in a photosensitive material,
such as a photoresist, photosensitive polymide, or similar. Such patterns
may be written either to be used directly as optical, mechanical,
fluidic, etc. components, e.g. diffusors, non-reflecting surfaces,
Fresnel lenses and Fresnel prisms, computer-generated holograms, lenslet
arrays, etc, or to be used as masters for the fabrication of such
components by replication. Replication can be done by molding, pressing,
embossing, electroplating, etching, as known in the art. This disclosure
includes descriptions of using passive absorbing components in thin
resist, using high gamma thick resists with high resolution pattern
generators, using multiple focal planes including at least one focal
plane in the bottom half of the resist, and iterative simulation of
patterning and adjustment of an exposure map.

Claims:

1. A method of forming a three-dimensional latent image with good depth
and shape control in a layer of resist applied over a workpiece surface,
the method including:converting a relief map that represents a
three-dimensional surface into point-by-point exposure doses calculated
to exceed an exposure threshold of the resist at a plurality of
controlled depths within the resist layer, producing an exposure map;
andrepeating for two or more iterations,simulating the patterning of the
resist layer with a pattern generator that varies effective exposure
doses on a point-by-point basis using the exposure map to produce a
simulated three-dimensional latent image,comparing the simulated
three-dimensional latent image to the relief map, andautomatically
revising the exposure map using results of the comparing.

2. The method of claim 1, wherein the method further includes repeating
for five or more iterations.

3. The method of claim 1, wherein the converting further includes
calculating a sweep adjustment that takes into account a direction of
travel of exposing radiation across the resist layer and compensating for
non-linear effects related to whether exposure is building or diminishing
as the exposing radiation moves across the resist layer, and
incorporating the calculated sweep adjustment into the exposure map.

4. The method of claim 2, wherein the simulating takes into account a
direction of travel of exposing radiation across the resist layer and
non-linear effects related to whether exposure is building or diminishing
as the exposing radiation moves across the resist layer.

5. The method of claim 1, wherein the resist is a positive resist that
includes a bleachable absorption component that is converted by the
exposing radiation and substantially loses it absorptiveness during the
patterning, whereby the bleachable components cause a linear relationship
between exposure energy (E) and the depth of exposure (D).

6. The method of claim 1, wherein the resist is a positive resist that
includes an effective quantity of passive absorption component that
absorbs photons without chemically exposing the positive resist, whereby
the passive absorption component causes a log-linear relationship between
exposure energy (E) and the depth of exposure (D).

7. The method of claim 1, wherein the layer is a thick layer of resist,
further including:defining multiple focal planes at which to focus
exposing energy;converting the relief map into point-by-point and
layer-by-layer exposure doses, the exposure doses allocated by layer,
producing the exposure map; andsimulating the patterning of the resist
layer using the multiple focal planes.

8. The method of claim 7, further including automatically selecting a
number of focal planes based on detection of vertical corners in the
relief map.

9. The method of claim 8, further including automatically selecting
positions of one or more focal planes based on data in the relief map.

10. The method of claim 8, further including automatically selecting
positions of two or more focal planes based on data in the relief map.

11. The method of claim 8, wherein the thick resist layer has a vertical
thickness that is greater than or equal to 1.5 times a depth of focus of
the pattern generator during the patterning, wherein the depth of focus
is twice a Rayleigh range.

12. The method of claim 8, wherein the thick resist layer has a vertical
thickness that is greater than or equal to two times a depth of focus of
the pattern generator during the patterning, wherein the depth of focus
is a twice Rayleigh range.

13. The method of claim 1, wherein the resist is a positive resist that
has a gamma of 5 or greater.

14. The method of claim 7, wherein the simulating takes into account a
numerical aperture of the pattern generator when writing to the multiple
focal planes.

15. The method of claim 1, wherein the pattern generator is a high dynamic
range pattern generator that is calibrated to produce at least 1000 dose
steps between minimum and maximum exposure doses.

16. The method of claim 1, wherein the pattern generator is a high dynamic
range pattern generator that is configured to write at least 4000 dose
steps between minimum and maximum exposure dose.

17. The method of claim 1, wherein the pattern generator is a high dynamic
range pattern generator that represents the relief map to a precision of
at least 11 binary bits and uses the 11-bit precision to produce exposure
doses.

18. The method of claim 1, further including patterning the resist layer
to form a three-dimensional latent image using a pattern generator that
varies effective exposure doses on a point-by-point basis using the
exposure map.

19. The method of claim 18, wherein the pattern generator is a laser
pattern generator.

20. The method of claim 1, further including repeating the simulating,
comparing and revising actions until the comparing results in a
difference between successive simulated three-dimensional latent images
that satisfies a pre-determined criterion

21. The method of claim 1, wherein the converting further takes into
account and compensates for non-linear effects related to feature
precision requirements, feature area and/or the gradient field.

22. The method of claim 1, wherein the converting further takes into
account and compensates for etch rate or dissolution rate selected.

23. The method of claim 1, wherein the converting further takes into
account and compensates for the etch rate or dissolution rate selected.

24. The method of claim 1, wherein the converting further uses
pre-determined rules and/or a model to compensate for non-linear effects.

[0002]This application further claims the benefit of U.S. Provisional
Application No. 61/107,588, entitled "Method of Compensation for
Bleaching of Resist During Three-Dimensional Exposure of Resist," filed
on 22 Oct. 2008.

[0003]The application further claims the benefit of U.S. Provisional
Application No. 61/107,591, entitled "Multi-Focus Method of Enhanced
Three-Dimensional Exposure of Resist," filed on 22 Oct. 2008. All these
provisional applications are hereby incorporated by reference for all
purposes.

[0004]This is one of three applications filed contemporaneously. The three
are entitled, "Method of Iterative Compensation for Non-Linear Effects in
Three-Dimensional Exposure of Resist," application Ser. No. ______;
"Method of Compensation for Bleaching of Resist During Three-Dimensional
Exposure of Resist," application Ser. No. ______; and "Multi-Focus Method
of Enhanced Three-Dimensional Exposure of Resist," application Ser. No.
______.

[0005]Three PCT applications of the same titles also have been filed in
English and designating the United States on Oct. 21, 2009 by applicant
Micronic Laser Systems. The contemporaneously filed US applications and
recently filed PCT applications are hereby incorporated by reference for
all purposes.

BACKGROUND OF THE INVENTION

[0006]The field of this disclosure is making three-dimensional topographic
structures by means of graduated exposure in a positive-tone
photosensitive material, such as a photoresist, photosensitive polymide,
or similar. Typically the produced surfaces have a surface profile which
is non-reentrant, i.e. for each lateral point (x, y) the surface has only
one height z(x,y) or there may be points where the surface is
approximately vertical (perpendicular to the xy plane). Alternatively
they may be said to have only positive slopes (including approximately 90
degrees to the xy plane, but no significantly negative (overhanging)
slopes. The surfaces may be called 2.5D surfaces since they have more
dimensions than the xy plane, but are significantly more constrained than
a 3D surface. Many relevant surfaces will have only positive slopes.

[0007]Such 2.5D patterns may be written in positive resist either to be
used directly as optical, mechanical, fluidic, etc. components, e.g.
diffusors, non-reflecting surfaces, Fresnel lenses and Fresnel prisms,
computer-generated holograms, lenslet arrays, etc, or to be used as
masters for the fabrication of such components by replication.
Replication can be done by molding, pressing, embossing, electroplating,
etching, as known in the art.

[0009]FIG. 1 shows a process for creating a 2.5D surface structure on a
workpiece by means of varying exposure of a photoresist as known in the
art. In FIG. 1a, a positive-tone photoresist 101 is applied to a
workpiece 102. In FIG. 1b, the resist is exposed to electromagnetic
radiation 103 with higher 104 and lower 105 exposure dose in an exposure
system 106. In FIG. 1c, the developer 107 dissolves part of the resist.
Areas exposed to a higher dose 104 dissolve faster than areas exposed
with less dose 105, creating a three-dimensional surface pattern 108, as
depicted in FIG. 1d. The profile can be used directly (as shown in FIG.,
scattering light in a controlled fashion.) It can be transferred into a
material with more durable or otherwise more suitable properties 109, as
in FIG. 1f. It can be used for replication of the three-dimensional
pattern 110, as shown in FIG. 1g.

[0010]Positive tone in this disclosure means that the developer removes
resist that is exposed above a certain dose, the threshold. Resists with
high contrast (high gamma) have a sharp on-set of dissolution at the
threshold dose, while for resist with low contrast (low gamma) the
dissolution rate is more proportional to the dose. This is illustrated in
the article, "Exposure of Photo Resists," supra, available at
http://www.microchemicals.eu/technical-information. The article posits
that grey scale lithography uses low contrast resist, rather than high
contrast resist.

[0011]Negative-tone resists, e.g., SU-8, become insoluble with increasing
exposure dose. Since there is always some absorption in the resist the
dose is higher at the top surface than close to the substrate, and it is
only when the resist is fully exposed that it will adhere to the
substrate after development. Partially exposed features or areas will
fall off or peel during development or rinsing. Therefore negative-tone
resists tend to be less suitable to the writing of 2.5D surfaces.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012]FIG. 1 shows a process to make a three-dimensional pattern in a
positive resist as known in the art. In FIG. 1a, a photoresist 101 is
applied to a workpiece 102.

[0013]The resist is exposed to electromagnetic radiation 103 with higher
104 and lower 105 exposure dose in an exposure system 106, FIG. 1b.

[0016]The profile can be used directly (here shown to scatter light in a
controlled fashion, FIG. 1e), transferred into a material with more
durable or otherwise more suitable properties 109, FIG. 1f, and/or used
for replication of the three-dimensional pattern 110 as shown in FIG. 1g.

[0017]FIG. 2a shows a diagram of the dissolution rate versus dose for two
different resist-developer systems.

[0018]FIG. 2b shows a diagram of the remaining resist thickness after
development of the two resist systems in FIG. 2a.

[0019]FIG. 2c shows the dose sensitivity of the resists in FIG. 2a.

[0020]FIG. 3a shows a diagram of the remaining resist thickness after
development of a resist dominated by bleaching.

[0021]FIG. 3b shows the dose sensitivity of the resists in FIG. 3a.

[0022]FIG. 4a shows a diagram of the remaining resist thickness after
development of a resist dominated by absorption.

[0023]FIG. 4b shows the dose sensitivity of the resists in FIG. 4a.

[0024]FIG. 5 depicts a simulated semi-sphere, after development, written
using a laser scanning system and 20 μm thick resist.

[0025]FIG. 6 depicts improved faithfulness of the latent image to the
ideal, after 5 iterations of simulation and exposure adjustment.

[0026]FIGS. 7-8 depict uncorrected and corrected exposure to produce a
latent image with one box set on top of another. FIG. 7 shows the result
of applying an exposure that matches desired result.

[0027]FIG. 8 depicts the improved exposure pattern and result after 10
iterations of modeling and exposure pattern adjustment.

[0028]FIGS. 9-10 depict uncorrected and corrected exposure to produce a
latent image of three rounded features in a row. FIG. 9 shows the result
of applying an exposure that matches desired result.

[0032]FIG. 13 illustrates compensation based on the data collection
illustrated by FIG. 12 and result of this compensation.

[0033]FIG. 14 illustrates M=3 different planes.

[0034]FIG. 15 adds to FIG. 14 a representation of varying pixel sized in
different exposure phases.

[0035]FIGS. 16 and 17A depict beam divergence patterns in resist layers
that are 1 and 80 μm thick, respectively. FIG. 17B is an enlargement
of a section of the 80 μm thick resist divergence pattern, that shows
a section 5 μm thick, from the center of the thicker layer.

[0036]FIG. 18 shows the difference between ideal and exposed in a 20 μm
resist layer, when the focal plane is set at 10 μm.

[0041]FIG. 24 illustrates alternative partitions between focal planes, in
cases of one and two writing passes.

[0042]FIG. 25 shows a flow chart of a focal plane algorithm.

[0043]FIG. 26 depicts a method and device for writing thin resist.

[0044]FIG. 27 extends the method and device of FIG. 26 to thick resist.

[0045]FIG. 28 depicts writing to multiple focal planes, which could be in
either thin or thick resist.

[0046]FIG. 29 depicts iterative refinement of an exposure map.

DETAILED DESCRIPTION

[0047]The following detailed description is made with reference to the
figures. Preferred embodiments are described to illustrate the present
invention, not to limit its scope, which is defined by the claims. Those
of ordinary skill in the art will recognize a variety of equivalent
variations on the description that follows.

[0048]Creating a three-dimensional profile in a resist is a non-linear
process, which means that the depth of resist removed by development is
not linearly proportional to the exposure dose. Instead, the input
pattern may be specified as a depth after development and a method may be
applied to translate the specified depth into an exposure dose, e.g. by
using a calibrated look-up table or mathematic expression. The exposure
dose creates a latent image that is developed in an effort to give the
desired depth profile.

[0049]A small variation in amounts of exposure dose gives a relatively
small change in dissolution rate during development, but not a linearly
proportional change. In prior processes, it is difficult to control the
depth with an accuracy of +/-1%, which may be required for optical
surfaces. The depth after development will be affected by small
disturbances, such as the baking temperature of the resist, fluctuations
of the laser power, thickness variations of the resist, agitation of the
developer, etc. The dose errors are often lumped together with
sensitivity fluctuations and developer activity variations. The combined
equivalent dose error is typically within the range of 1-5%. The prior
process is based on close control of the dissolution rate in the
developer by the exposure dose is difficult to keep stable and often
needs frequent recalibrations. Even with recalibration, a process that
depends on a closely controlled dissolution rate and time without
automatically compensating for non-linear effects, such as bleaching
effects, will not consistently produce results within +/-1% of the ideal
feature.

[0050]The problem with the prior process depicted in FIG. 1 is its
sensitivity to disturbances. Slight variations in the dose, such as
variations due to laser noise, and variations in the resist properties or
the developer agitation, cause depth variations in the finished profile.
Likewise, the time and temperature control during development is
critical.

[0051]An opportunity arises to introduce new processes for controlling the
depth and shape of features exposed in a relatively thick resist layer,
preferably with an accuracy of +/-1%. Better, more easily controlled 2.5D
feature formation may result.

[0052]The relationship between exposure dose and relief height is complex
and involves non-linear effects. The problem underlying the herewith
presented invention is to be seen in providing a method of forming a
three-dimensional latent image with good depth and shape control in a
layer of resist. By iteration, the present invention automatically
improves on and refines the exposure dose for a particular relief map. In
addition, the method disclosed herein automatically takes into account
non-linear effects in the resist. Two or more iterations may be used for
producing the exposure map with point-to-point exposure dose calculated
to exceed an exposure threshold of the resist at a plurality of
controlled depths within the resist layer. By simulating the patterning
of the resist layer and comparing the simulated three-dimensional latent
image to the relief map, the dose levels of the exposure map are adjusted
as a result of the comparing step.

[0053]According to certain embodiments of the present invention,
pre-determined rules or a model of the exposure and development process
may be used to compensate for non-linear effects. The rule-based, or
model-based, compensation may automatically adjust the gray-scale values,
e.g. the gray-scale values of the modulator pixels of the pattern
generator, as a function of feature precision requirements, feature area
and/or the gradient field. The height information for the exposure
pattern may be adjusted by the rules or the model, either mathematically
or in grey scale, e.g. by automatically adjusting the modulator
gray-scale values of the pattern generator used for exposing the resist.
In order to speed up the iterative method proposed above, a rule-based
model may be used to give a first exposure map converted from the relief
map and with initial exposure dose levels as the initial input to the
iterative loop of simulating the exposure map by repeatedly comparing the
simulated exposure map to the relief map.

[0054]The etch rate (or dissolution rate) selected, e.g. in a DRIE
process, may give different z-depths for patterns with different feature
precision requirements, feature areas and/or gradient fields, even if the
patterns have the same z-depth in the relief map, e.g. a CAD pattern,
representing the three-dimensional surface. The above-mentioned
rule-based, or model-based, compensation may also compensate for the etch
rate, or dissolution rate, selected.

[0055]When translating relief depths to exposure doses in a scanning
system, the asymmetry related to the sweep direction of a scanning
writing laser beam exposing the resist may be taken into account and be
compensated for, e.g. including sensitivity of exposure to whether the
exposing energy is waxing or waning. In a raster-scan pattern generator,
there is a difference between a first feature edge (change from no dose
to high dose), and the second edge (change from high dose to no dose.) In
the direction of scanning, and since the exposing beam spot has a finite
width, the first encountered edge will receive a lower dose than the
second edge. The second edge will absorb slightly less dose than the
first edge, since it has already been partly bleached by the light
exposing the previous position or pixel. This will create an effective
tilt in the exposure. Whether it is a first or a second feature edge that
is exposed may also be automatically compensated for according to certain
embodiments of the present invention. Other issues that may be usefully
addressed by introducing pre-determined rules and/or a compensation model
when translating relief depths to exposure doses include absorption of
exposure doses, and photonic and chemical/physical processes in exposure
and development.

Background on 2.5D Exposure

[0056]We disclose methods to generate three-dimensional microstructures,
or nanostructures, using direct laser writing in a thick photoresist
layer. Many of these surfaces are 2.5D or non-reentrant surfaces as
defined above. One way previously described to manufacture such
structures is to use a pre-fabricated photo-mask having a grey scale
pattern, and expose the photoresist through that mask for a sufficient
time to reach a sufficient exposure dose [mJ/cm2]. In direct writing
using an optical pattern generator, on the other hand, the exposing dose
may be a limiting factor. By superposition of N separate exposure passes,
sufficient dose can be applied to create the desired latent image in the
resist.

[0057]The N-pass writing is further utilized as a means for averaging out
several different possible pattern-deteriorating effects labeled by the
Japanese word Mura. Improved performance in all three dimensions (x, y,
z) can be achieved by shifting the writing grid an appropriate distance
in both the x- and y-directions. The exposure doses are set from resist
depth-vs-dose characteristics, which take into consideration the
non-linear depth-to-dose relationship, and absorption, bleaching and
defocus properties in the photoresist.

Writing Systems

[0058]The writing system used is a direct-writing pattern generator, in
contrast to systems that use masks as an intermediate step. The
direct-writing system converts an input description of the 2.5D pattern,
e.g., a list of (x, y, z) coordinates, to a bitmap and writes the bitmap,
suitably converted to expose the resist. The writing system has a stage
for holding the workpiece, a source of electromagnetic radiation in the
range of 460 nm or less, e.g., a laser at approximately 413, 364, 355, or
266 nm wavelength. It includes focusing optics and a modulator for the
radiation. Several architectures are possible: scanning one or several
beams with an acoustooptic or mechanical scanner, scanning the stage
under an array of projected light spots, scanning the stage in relation
the image of a spatial light modulator, either projecting a 1D line or 2D
area of contiguous modulated pixels, or an array of light spots
individually modulated. What is more important than the actual mode of
scanning or creation of the image is to have a high dynamic range and,
preferably, a high maximum dose.

[0059]Suitable modulators include acoustooptic and electrooptic modulators
and directly modulated lasers. micromechanical Spatial Light Modulators
(SLMs) such as Grating Light Valves (GLVs from Silicon Light Machines)
and Digital Mirror Devices (DMDs from Texas Instruments) as well as
analog SLMs (from Micronic Laser Systems and Lucent) also may be
suitable. Analog SLMs may rely on either tilting or piston driven
mirrors. Either configuration may render shades of grey due to
destructive interference effects.

Multi-Pass Writing

[0060]Binary modulators such as the DMD may achieve high-dynamic range
grey-scale modulation first by having 10,000:1 or better contrast, and
secondly by writing many passes with different doses, e.g., with doses
corresponding to powers of two. A pattern of 12-bit grey values may be
written in 12 binary passes. It may be beneficial to use even more
passes, such that the binary passes with highest dose are subdivided into
multiple passes which build up the high dose gradually. If the total dose
is higher than approximately two times the maximum dose that can be
delivered in a pass several passes at high dose can be used to accumulate
the needed dose. Additional passes with less dosage may be used in a
hybrid multi-pass scheme to get any dose value less than the maximum
dose. For example, a six-bit grey value in the range 0-127 units might in
this way be written in a writer capable of delivering maximum 16 units
per pass, by combining in a hybrid multi-pass scheme a number of
high-dose passes (here 7 passes) with a number of passes with lower dose
(4 passes). Any dose in the range 1-127 units can thus be written in 11
binary passes with the doses 1+2+4+8+16+(16+16)+(16+16+16+16). This
allows higher doses to be deposited in the resist than either the resist
or the writing system is capable of in a single pass. Alternatively,
binary writing passes may gain grey scale precision by using passes with
less than a factor of two in difference, such as a factor of the square
root of three: 1.0, 1.7, 3.0, 5.4, 9.0 units. A sequence with less than a
factor of two grey scale differences may have more than one possible
representation for a grey value; it is possible to choose the one which
adds up closest to the actual grey value. In the sequence above, with a
step of sqrt(3), the value 10 can be approximately represented as 1.0+9.0
or 1.7+3.0+5.4. During calibration, the dose sum that best represents the
value 10, for instance, using the actual values in the multipass scheme
can be chosen. The passes with less than a factor of two difference may
be combined into a hybrid multi-pass scheme. For instance, passes of 1.0,
1.7, 3.0, 5.4 dose units plus ten passes with a 9.0 dose can span a range
of 1-100 dose units, using a writer that delivers up to 9 dose units in a
single pass.

[0061]Exposure with scanning laser light may be modeled as Gaussian beams
with a Gaussian intensity distribution. Other optical power density
distributions are naturally possible. The beam, or beams in a multi-beam
writer, can be focused in the laser writer tool's final lens system
either on the upper surface of the photoresist, or somewhere between the
resist surface and the substrate surface in the downwards z-direction.
During propagation through the photoresist layer, a Gaussian beam
diverges (widens) due to its wave property, making the resulting lateral
(x, y) as well as vertical (z) writing resolution deteriorate. The
depth-of-focus is determined by the numerical aperture (NA) of the lens
system of the writer system, together with the refractive index of the
photoresist and of the ambient medium. Furthermore, the power density or
deposited/absorbed exposure dose varies with the depth in the resist.

[0062]In generation of some 2.5D structures by direct-write (laser)
lithography, the resist may be much thicker than in ordinary 2D
microlithography, such as lithography to produce semiconductor circuits
and LCD or OLED displays. When the photoresist is thicker than the
depth-of-focus of the writer tool, the spot size varies by depth
(z-level) in the photoresist.

[0063]The iterative modeling and dose selection part of this disclosure
discloses methods of compensating for linear and non-linear response to
exposing radiation of a relatively thick resist layer. When 2.5D
patterning of thick resist is addressed, nonlinear effects become
important.

[0064]Bleaching is one of the nonlinear effects. By bleaching, we mean a
change in the optical absorption of a resist as it is exposed to
radiation. This bleaching may result from absorption of energy and may
also depend on the time between exposure passes or other phenomena.

[0065]A second kind of optical absorption does not expose the resist; it
converts photons to heat. Dyes, pigments or nano-particles in resist have
this effect, as well as some of the chemical agents making up the resist.
With non-bleachable absorption, the exposure dose required becomes
exponential with depth.

[0066]Multi-focal plane exposure is a method of compensating for the
thickness of a thick resist layer and/or improving the fidelity of
three-dimensional patterning. Multi-focus involves focusing at various
depths in the resist, such as at the top, in the middle, and near the
bottom, and assigning varying amounts of exposure dose to each of the
focal planes. For modestly thick resist layers, a single focal plane may
be sufficient, positioned between the top and bottom of the resist layer.
Often, a single focal plane in the bottom half of the resist, away from
the exposed surface, will produce favorable results for reasons explained
below.

[0067]The iterative modeling approach can readily take into account
bleaching, dye and/or multi-focus exposure. Bleaching and dye can be
taken into account when choosing how to apply multi-focus exposure,
particularly as the top portion of the resist bleaches.

Iterative Analysis and Exposure after Modeling

[0068]Issues that can usefully be addressed when translating relief depths
to exposure doses include asymmetrical response to the sweep direction of
scanning writing laser beams, absorption of exposure doses, and photonic
and chemical/physical processes in exposure and development.

[0069]One of the problems in 2.5D microlithography is asymmetry related to
the scan direction of an exposing laser beam, i.e. sensitivity of
exposure to whether the exposing energy is waxing or waning. In a
raster-scan pattern generator, there is a difference between a first
feature edge (change from no dose to high dose), and the second edge
(change from high dose to no dose.) In the direction of scanning, and
since the exposing beam spot has a finite width, the first encountered
edge will receive a lower dose than the second edge. The second edge will
absorb slightly less dose than the first edge, since it has already been
partly bleached by the light exposing the previous position or pixel.
This will create an effective tilt in the exposure. FIG. 5 depicts a
simulated semi-sphere, after development, written using a laser scanning
system and 20 μm thick resist. The scan is proceeding from left to
right, so that left hand side of the semi-sphere is exposed first. The
resist model used to simulate the dynamic system takes into account
bleaching of the resist. The semi-sphere is the ideal, desired shape of
the resist after development and, therefore, the desired shape of the
latent image after exposure and before development. As the simulation
shows, a pattern of exposing radiation that matches the ideal pattern
produces a latent image that is skewed to the left. This is readily
apparent in the difference graph in the middle of FIG. 5, which shows
that the difference is asymmetrical between the left and right edges of
the feature.

[0070]A dynamic model of 2.5D latent image formation can take into account
at least three exposure-energy-absorbing processes. First,
αExp non-bleaching absorption leading to developable
exposures, ordinarily created by the concentration of the Photo-Active
Compound (PAC). Second, αExp, Bleach leading to developable
exposures with a component that is so-called bleachable, that has an
absorption that diminishes with increasing absorbed exposure dose. This
can be mathematically expressed as a linear approximation using two
derivatives:

∂ α Exp ∂ z or
∂ α Exp ∂ D ##EQU00001##

where D is the exposure dose. Thus, one may express the change of the
bleachable absorption as:

[0071]A third energy absorption component, represented by αDye
converts absorbed photon energy to heat, rather than resist development.
A dye or another photon absorbing substance in the resist has this
effect.

[0072]The response to the exposing light/radiation in the photoresist may
be separated generally into photonic and chemical/physical effects. The
photonic effects, include an inherent proximity effect caused by the
convergence and divergence of the focused light in the photoresist, light
scattering in the optical system, light scattering in the photoresist,
reflections at the substrate etc. The chemical/physical effects include
the influence from the soft-bake of the resist, the dehydration and
rehydration of the resist, the photo-chemical reactions during the
exposure, the physical-chemical diffusion processes during and after the
exposure, and the concentration-, temperature- and agitation-influences
during the development.

[0073]Examples of Iterative Adjustment of Exposure

[0074]FIG. 6 depicts improved faithfulness of the latent image to the
ideal, after 5 iterations of simulation and exposure adjustment. The
ideal and exposed patterns are virtually indistinguishable in the top
part of the figure, which is significant improvement over the results
depicted in FIG. 5. The scale of the difference graph in FIG. 6 is
adjusted from the scale in FIG. 5, because the difference is small. As
the bottom part of FIG. 6 shows, the exposure pattern is not a
semi-sphere after adjustment, but the exposed result in a latent image or
after development closely approximates the ideal.

[0075]FIGS. 7-8 depict uncorrected and corrected exposure to produce a
latent image with one box set on top of another. FIG. 7 shows the result
of applying an exposure that matches desired result. The exposing
radiation profile is shown at the bottom. The exposed result is compared
to the ideal at the top. The middle part of FIG. 7 shows the difference
in the exposed pattern, between ideal and actual.

[0076]FIG. 8 depicts the improved exposure pattern and result after 10
iterations of modeling and exposure pattern adjustment. The proximity
effects related to exposing a thick photo resist with a complex pattern
are corrected by iterative modeling and exposure adjustment.

[0077]FIGS. 9-10 depict uncorrected and corrected exposure to produce a
latent image of three rounded features in a row. FIG. 9 shows the result
of applying an exposure that matches desired result. The exposing
radiation profile is shown at the bottom. The exposed result is compared
to the ideal at the top. The middle part of FIG. 9 shows the difference
in the exposed pattern, between ideal and actual.

[0078]FIG. 10 depicts the improved exposure pattern and resulting latent
image after 10 iterations of modeling and exposure pattern adjustment. In
the top image of FIG. 10, the ideal and exposed patters are virtually the
proximity effects related to exposing of a thick photo resist with a
complex pattern corrected by iterative modeling and exposure adjustment.

[0079]In some circumstances, the exposure pattern is tentatively corrected
before the latent image is simulated. The algorithm provides rules and/or
a model of the exposure/development process. The result of this
tentatively corrected pattern is simulated and fed into an iterative
correction process. The iterative process can be repeated until the
residual improvement is below a pre-determined threshold.

[0080]The aforementioned algorithm is used to compensate for non-linear
photo resist processes such as bleaching. Accordingly, the algorithm
removes the extra proximity effects that occur for thick resist and a
high optical NA.

[0081]In other circumstances, the algorithm calculates the non-linear
effect in some directions in the XY plane and then calculates the total
correction as a linear combination of the result. The algorithm may
calculate the non-linear effect in one or a few directions in the XY
plane only and then calculate the total correction as a linear
combination of the result.

[0082]Impact of Etch Rate and Minimum Line Width Requirements

[0083]FIG. 11 illustrates use of a reduced etch rate to improve so-called
feature size, lateral dimension, or line width variation, which is also
sometimes referred to by the shorthand "CD" variation, for feature
critical dimension variation or accuracy. Changes in etch rate impact the
minimum line widths typically achieved. This is interrelated to the
feature area and gradient field in a pattern. The etch rate for a deep
reactive ion etch (DRIE) process is often treated as dependent on the
minimum line widths or feature sizes and the gradient field in the area
etched. The dissolution or removal rate for some thick photoresists is a
function of the minimum line widths or feature sizes and the gradient
field, as shown in FIG. 6. Depending on the etch rate selected, the
etching in a DRIE process applied to thick photoresists will give
different z-depths for patterns with different feature precision
requirements, feature areas and gradient fields, even if the patterns
have the same z-depth in the CAD-pattern.

[0084]FIG. 12 illustrates collecting data regarding the effect of etch
rate as function of feature CD. The relationship between the etch rate
(or dissolution rate) and the feature precision requirement, feature area
and gradient field is first identified, before compensation is applied.
From this data, a rule-based (or model-based) compensation model is
created that adjusts the grey-scale as a function of feature precision
requirement, feature area and gradient field. The feature precision
requirement and/or similar measurements such as the feature area and/or
gradient field are then calculated. Thus, from the function identified
above, changes are made in height information for the pattern. This may
be done either mathematically or in grey scale. After the adjustment is
made, each pattern will get the correct depth independently of the
feature CD. Finally, the modified pattern is written.

[0085]The proximity effect is caused by the convergence and divergence of
the focused light. By exposing areas that are large compared to the
proximity effect, and by measuring the depths in the central regions of
such exposed areas for a certain combination of spot size and grid size,
the proximity effect influence is measured and can be compensated. The
resulting depth-vs-dose characteristics for the photoresist are then more
or less dominated by the photo-chemical effects. The proximity
effect-related processes are handled by proximity effect correction and
compensation methods.

[0086]FIG. 13 illustrates compensation based on the data collection
illustrated by FIG. 12 and result of this compensation. It illustrates
adjusting the exposure dose to change the z-dynamics of the exposed
pattern. Exposure of a (positive) photoresist may or may not encounter a
bleachable PAC. In the development of a positive photoresist, each dose
level is dissolved (etched) with a rate that is a function of, and
increases with, the dose. In timed, rate-dependent processes, control of
the etch depth d=d(D) requires careful control of development time
TDev. Erroneous TDev results in erroneous relief depth d and
erroneous relief swing Δd. The dissolution rates are also affected
by the developer concentration, the developer temperature, the
development agitation by flushing, stirring etc., which helps maintain
fresh developer at the resist surface and avoid accumulation of diffusion
barrier of dissolved resist in the developer. Given these factors, it is
useful for control of relief depths to depend primarily on controlling
the exposure dose.

[0087]We disclose an alternative for depth control of 2.5D reliefs that
involves an end point approach to developing resist. In a high-absorption
photoresist that is fully developed until the etch rates have decreased
at least close to zero, the depths are relatively insensitive to the (i)
development time, (ii) developer concentration, (iii) developer
temperature, or (iv) development agitation by flushing, stirring, etc.
Instead, the depths depend most heavily on the exposure dose and its
precision.

Introduction to Bleaching and Multiple Absorption Processes

[0088]Iterative compensation can be applied to a variety of process
factors, beyond exposure dose.

[0089]For some purposes, a resist with high absorption αExp is
useful. The high absorption αExp resist may be bleachable. For
simplicity, the result of exposure may be described as a "tube" of
constant width through the resist, with due to the higher absorption fast
decaying dose with depth. FIG. 16 illustrates a "tube" of exposed resist.
At a certain depth, different for different doses, the exposing number
[cm-3] of photons has decreased to a level where the development
dissolution rate approaches zero. Development means that every dose level
is dissolved with a both in time, and thus for different resulting
depths, varying dissolution rate. In resist thicker than the exposed
depth, the dissolution rate decreases with increasing depth and
approaches zero. Full development involves development time that allows
the dissolution rate to go close to zero for the deepest relief levels,
where the highest exposure dose was applied to decrease the greatest
feature depth. With extended development, the control of the final resist
depths for different doses is governed and controlled by the exposure
dose (due to the high absorption) and not the development time. The exact
exposure dose is controlled in the exposure tool.

[0090]In other circumstances, a resist with at least two absorption
processes is used. The first absorption process described by the
coefficient αExp or αExp, Bleach results exposure
of the resist and formation of the latent image, with bleaching of a
first absorbing component. The second absorption process,
αDye, increases absorption, but does not contribute to the
exposure of the resist. That can be achieved using dyed or colored or
pigmented resist additives.

[0091]The control of the final resist depths for different doses can be
governed and controlled by the exposure dose due to the high absorption,
with reduced sensitivity to development time and conditions. An advantage
of using the exposure dose is that the photon absorption and depletion is
not controlled by the same absorption process responsible for the
exposure, a process which is also bleachable.

[0092]The second absorption process αDye must be balanced
against the available photon flux, i.e. the maximum available exposure
dose, the exposure absorptions αExp or αExp,
Bleach, the desired maximum relief depth and the desired relief swing.

[0093]If the combined absorption coefficients are too high, then the
desired relief depth cannot be reached at full development, because the
available does at depth is too small. If the total absorption results are
too low then the dissolution rate(s) and the final relief depths will be
controlled by the development time, which is undesired. A useful
combination of absorption coefficients can be obtained by chemical
tailoring of the various absorption processes to available number of
photons and the relief to be fabricated.

[0094]The various absorption processes can be combined in many ways
including:

[0095](i) αExp or αExp, Bleach low, and
αDye high.

[0096](ii) αExp or αExp, Bleach high, and
αDye low.

[0097]Both alternatives may result in a high total absorption. The second
alternative should lead to reduced requirement on available photons,
which is useful when available exposure dose is a limiting factor. The
absorption level becomes high and the dose is limiting when the resist
thickness is increased.

[0098]Refractive Index and Depth of Focus

[0099]Exposure of a thick resist is difficult when the film thickness is
substantially larger than the depth-of-focus of the focus system of the
exposure tool. For example, if the laser light is focused at the upper
surface of the photoresist, the laser light or beam will--after the
focus--start to diverge, to widen. Deeper resist regions will be exposed
by a wider light beam that shallower regions. Due to Snell's law of
refraction and the fact that photoresist has a higher refractive index
nR that an ordinary gas ambient such as air or nitrogen, the
depth-of-focus in the resist will be larger than in the atmosphere.
Accordingly, it is useful for a resist to have as high nR as
possible. A second target is to adapt the bleaching properties of the
photoresist, which depends on the exposure dose, so that the refractive
index of the resist does not change too rapidly or too slowly with the
absorbed exposure dose and consequent bleaching. The appropriate
characteristics of a particular resist can be determined by exposing
areas of constant dose, with widths bigger than the proximity effect
effective distance, and by accurately measuring the depths after
development for the various doses. This yields depth-vs-dose
characteristics of the resist, which may be expressed as d=d(D). The
characteristics may include all non-linear effects as well as bleaching.

Particular Use Cases

[0100]By carefully choosing parameters for the exposable absorption
processes αExp and the non-exposable processes
αThermal, and αExp, Bleach, the resulting process
may be tuned and the performance of the 2.5D-relief generating tool will
be greatly improved.

[0101]In some circumstances, the photo-sensitive material is given a high
exposure-active absorption via the PAC. The development process may be
"terminated" at a certain depth level where all the exposing energy has
been depleted. This requires that the amount of exposing energy is not a
limiting factor.

[0102]According to yet another embodiment, when the amount of exposing
energy is not a limiting factor, the photo-sensitive material is exposed
to a pre-determined absorbed dose. The photo-sensitive material is then
developed until the development process ceases at a certain depth in the
photo-sensitive material where there no longer is any exposure energy
available due to the exposable absorption.

[0104]The technology described in this disclosure provides methods to
control a three-dimensional photoresist process better than those known
in the art.

[0105]FIG. 2 shows the dissolution properties of two fictitious but
typical resists used for microlithography (Resist A) and
three-dimensional processing (Resist B). Resist A and its process
conditions are chosen to give a high gamma and Resist B a low gamma.
Gamma γ is a measure of how fast the dissolution rate changes for a
small change of exposure dose, i.e.

γ=(dR/R)/(dE/E)

[0106]where R is the dissolution rate as expressed by nm/s and E is the
exposure dose as expressed in mJ/cm2. Gamma is a unit-less number
and does not depend on the units chosen to express R and E. There exist
several definitions of gamma, each determined by a different type of
measurement. In Mack C., Fundamentals Principles of Optical Lithography,
Wiley (2007) the author describes in chapter 7.2 what he calls "measured
contrast" or γm, determined from the remaining thickness after
development as a function of dose:

γ m = 1 D z ( ln E ) E = E
0 ( Mack 7.21 ) ##EQU00003##

where D is the full thickness, z the remaining thickness, and E the
exposure dose and E0 the dose where the resist just clears (all
resist is removed in the developer). Another measure is the theoretical
contrast γth, based on dissolution rate instead of thickness:

γ th = ( ln R ) ( ln E ) (
Mack 7.22 ) ##EQU00004##

where R is the dissolution rate in the developer. We adopt this equation
as the gamma definition used in this disclosure, i.e. a resist specified
to have a gamma of 5 or higher in this disclosure has--in the terminology
of Mack--a theoretical contrast of 5 or higher. It can be determined by
measuring how deep the developer has dissolved the resist in areas with
known exposure after a fixed period of time. Mack says that if the
development rate varies with the depth into the resist, the measured
contrast fails to give a good value for the theoretical contrast. He
gives two examples, namely the cases of surface inhibition and of
absorbing resist. In the case of passively absorbing (non-bleaching)
resist Mack gives a relation:

γ m = γ th ( 1 - - α nD
α nD ) ( Mack 7.29 ) ##EQU00005##

Mack goes on to propose what he calls "practical contrast" denoted by
γ without any subscript. Practical contrast is based on the how
long it takes for the developer to remove the resist after it has been
exposed to varying doses. The theoretical contrast, which is the quantity
used in this disclosure, depends on the detailed chemistry during
dissolution of the resist in the developer.

[0107]Photoresists for binary processing, such as those used in
microlithography, are tuned to have a high gamma, i.e. 5, 8, 12, or even
20. These resists do not work well for three-dimensional processing, as
shown in FIG. 1. FIG. 2a shows a diagram of the dissolution rate versus
dose for two different resist-developer systems. Resist A in FIG. 2 has
gamma=8, which means that for low doses it has low dissolution rate, and
above a threshold dose the dissolution rate rises very rapidly. If the
resist is developed for a predetermined time, the thickness loss will be
proportional to the dissolution rate and the time, assuming that the dose
is uniform in the vertical direction. Typically, the development times
are fairly long so that the resist has essentially stopped dissolving any
resist at the end of development, sometimes called an endpoint. FIG. 2b
shows a diagram of the remaining resist thickness after development of
the two resist systems in FIG. 2a.

[0108]The remaining resist thickness in FIG. 2b is then a steep function
of the dose. FIG. 2c shows the change in thickness vs. change in relative
dose, i.e. (dD/(Dmax-Dmin))/(dE/E), and it is seen that with
Resist A the remaining thickness, i.e. the profile depth after
development, is very sensitive to dose and a 3% percent variation in dose
or sensitivity would give high variation in the thickness, since there is
an sensitivity that essentially diverges.

[0109]When making the three-dimensional patterns, the dissolution
typically is timed and not allowed to continue indefinitely. Therefore,
the profile depth is proportional to the development time, i.e.

(dD/D)/(dt/t)=1

where D is the depth and t is the development time. This process is called
a dissolution-limited process. The process is furthermore sensitive to
the temperature, e.g. the activity of the developer may double for every
7 degrees and this is magnified by the steepness of the dissolution
curve.

[0110]When making three-dimensional patterns with Resist A all the depth
change occurs at a very small dose range, e.g. only between 60-80% in the
diagram. With a modulator controlled by a DAC with typically 8 bits, only
a small range of the 256 codes would be used to control exposure dose.
Obviously, the process described above using a Resist A type resist as
the only resist is not well-suited for creating three-dimensional
patterns.

[0111]Resist B in FIG. 2 is a resist that those of ordinary skill would
expect to be used for three-dimensional processing. It has a gamma of 2,
which means that the dissolution curve in FIG. 2a is less steep. The
development time is also typically less. The remaining resist thickness
is also less steep. The dynamic range is larger, practically 20% to 100%
for the maximal dose might be used, since the top surface of the profile
is preferably placed some distance from the top of the resist due to the
in-homogeneity of the resist close to the surface caused by e.g. drying,
chemical segregation, etc. FIG. 2c shows the dose sensitivity of the
resists in FIG. 2a.

[0112]There will be a larger range of dose values used to create the depth
range and a 3% dose variation changes the remaining thickness by at most
3% as shown in FIG. 2c. The sensitivity to relative time changes is equal
to Resist A but the sensitivity to temperature is less inflated than for
Resist A. Overall, Resist B and the process described are more suitable
for creating 2.5D patterns, but still not stable and robust enough to
create patterns with depth accuracy requirements of 1% or less. Again,
the Resist B process described requires frequent recalibrations and
critical process tuning.

[0113]Process Dominated by Bleachable Absorption

[0114]FIG. 3a shows a diagram of the remaining resist thickness after
development of a resist dominated by bleaching. FIG. 3a shows a first
process in which the remaining thickness for Resist C is dominated by
bleaching, which we call a bleaching-limited process. Many common
resists, in particular DNQ-type positive resists, have an absorption rate
of 0.5 per micron or more. When the light exposes the resist, a
hydrophobic group is photochemically converted to a hydrophilic acid,
allowing the water-based developer access into the resist. The
photoconverted group has much less absorption after the conversion than
before it. The absorption bleaches strongly during exposure and is much
reduced. This is commonly described by so called Dill parameters which go
into a system of rate equations formulated by Rick Dill at IBM in 1975.
See, F. H. Dill, et al., "Characterization of positive photoresist," IEEE
Transactions on Electronic Devices, ED-22, 445-452. Dill parameters,
exposure and development of photoresist are discussed in many textbooks
on lithography; a recent text is C. Mack, Fundamental Principles of
Optical Lithography, Wiley, 2007. Optical absorption of various resists
is described in the article, "Photoresists Optical Paramaters," supra,
which indicates refractive indexes of 1.65-1.710, depending on wavelength
for a number of DNQ resists. Another article on the same site, "Exposure
Phtoresist," indicates sensitivity of various resists up to 460 nm.

[0115]In a thick resist, which is essentially non-transparent before the
exposure, the exposing dose initially reaches only into the first micron
or so at the top. After the top layer has been bleached, the light
reaches the layer below it and bleaches it. In this way the light works
its way into the resist. Since the energy to bleach one micron of resist
is the same regardless of the position in the resist, the depth to which
the resist is exposed and bleached is a linear function of the dose. At
development the resist will develop as far as it is exposed, and the
remaining thickness is a linear function of the dose. The thickness
change vs. the relative dose change has a different curve and is
generally more benign. As indicated in FIG. 3a, the dose to bleach the
resist is considerably higher than what is needed to expose the resist
without bleaching. FIG. 3a shows an example where the resist is exposed
from top-to-bottom at the dose 1000%, as compared to a 100% dose for a
non-bleaching and non-absorbing resist. FIG. 3 shows an idealized resist,
the actual values may differ in an actual process.

[0116]The process in FIG. 3a is suitably applied to a high-gamma resist,
such as Resist A in FIG. 2, with a long development time. The development
will then develop through the exposed and bleached part of the resist and
stop at a certain dose, which has a very low dissolution rate. The timing
and activity of the developer will have less influence on the remaining
depth and the control of the profiles will be better due to the more
linear depth vs. exposure curve. The result is a process which is more
robust and easier to use in an industrial setting.

[0117]Process Dominated by Passive Absorption

[0118]FIG. 4 shows a second process with Resist D, which is dominated by a
non-bleaching absorption, which we call an absorption-limited process.
Like Resist C, Resist D has high gamma and long development, so the
development reaches a point that is little influenced by time and
temperature during development. If the absorption is expressed by α
(with the unit per micron), the exposure at the depth D is

E(D)=E0exp(-αD)

[0119]where E0 is the exposure at the surface.

[0120]The relation can be inverted to give the depth where the exposure is
at the threshold dose Eth where with the actual development time the
developer effectively stops

D(Eth)=1/α*ln(E0/Eth)

or, simplified,

D=c1 ln(E)+c2

where c1 and c2 are constants which implicitly represent
α, the resist sensitivity and the development time.

[0121]FIG. 4a shows a diagram of the remaining resist thickness after
development of a resist dominated by absorption. FIG. 4b shows the dose
sensitivity of the resists in FIG. 4a.

[0122]FIG. 4b depicts the so-called absorption-limited process. The dose
sensitivity is much less than either the dissolution-limited or the
bleaching-limited process. The amount by which dose sensitivity is
suppressed depends on the relation between the profile depth Dmax
and the absorption α. The greater the value of α is, the less
sensitive the process is to relative dose and developer disturbances and
the better the process control is. However, the exposure dose needed is
higher. A significantly high value of α will require such strong
exposure that the resist may solarise. That is, the resist may reverse
its sensitivity and start getting more difficult to dissolve again, at
the top. Likewise, if the energy is deposited in a brief time, such as
using a laser pulse, the maximum dose may be limited by the allowable
heating. Therefore, it is desirable to have a range of resist
formulations with different α for different profile depths or
resist layer thicknesses. For a maximum profile depth of Dmax may in
different contexts have a value higher than 1.5/Dmax, 2/Dmax, 3/Dmax,
4/Dmax, or 5/Dmax, corresponding to a maximum writing dose of 4.5, 7.4,
20, 55, or 148 times higher than the dose that expose the top portion of
the profile. Obviously every writing system also has some practical,
thermal or throughput-related limit to the highest dose Emax which
puts an upper limit αmax on the absorption such as 1000, 300,
100, 30, or 10 times the dose used to expose the top of the profile
Emin. The value of αmax can be calculated as
ln(Emax/Emin)/Dmax. If Dmax is one micron then
α will have to be smaller than 6.9, 5.7, 4.6, 3.4, or 2.3 per
micron. In a different example, the Fresnel lens above where Dmax is
5 microns, α may be need to be smaller than 1.38, 1.14, 0.92, 0.68,
or 0.46 per micron.

[0123]The absorption should preferably be matched to the resist thickness
and the dynamic range of the writing system. One way of doing this is by
the selection of existing resists, e.g., dyed or colored resists. Another
way is by adapting the writing wavelength to specific profile heights and
resists. A third approach is to add a passive or bleachable absorbing
compound to the resist formulation.

[0124]The scales are different in FIGS. 2b, 3a, and 4a, in order to
highlight the basic function of each resist and process. A real resist
and resist process will have both absorption and bleaching. The depth of
development will be affected by the finite dissolution rate. The
dissolution rate alone gives a depth increasing faster than proportional
to the exposure dose. A so-called bleaching resist will have a linear
relation between depth and dose. A so-called absorbing resist will have a
depth function that grows slower than proportional with the dose. The
more that the absorption dominates, the more the depth vs. dose will
resemble a logarithmic curve. Piecewise, we may express the depth as
proportional to the dose raised to a constant k.

D(E)=k1Ek

where k1 is a proportionality constant. One way to classify the
resist processes is to name them according to the value of k:

[0125]Dissolution-like: k>1.5

[0126]Bleaching-like: 0.5<k<1.5

[0127]Absorption-like. k<0.5

Fresnel Lens Example

[0128]An example is that of the making of a Fresnel lens. The profile
depth is 5 microns and the required wavefront error is lambda/4
peak-to-valley at 400 nm, i.e. +/-50 nm or +/-1% of the profile depth.
Assume we need to write the Fresnel lens pattern with a profile depth of
5 microns. The depth inaccuracy needs to be +/-50 nm or +/-1% of the full
depth. If the limit on dose Emax is 100 times Emin α can
be up to 0.92 per micron. We can directly use the diagram in FIG. 4a for
Emax/Emin=100 and find that the dose sensitivity is 0.22% of the full
depth per % relative dose change. The allowed dose variation is then
1/0.22=5%, This is well better than the writing and development system's
3% control and we can actually select a resist that has a lower α,
e.g. α=0.64 per micron or we can use α=0.92 per micron and
produce surfaces with three times better depth control, e.g. <+/-0.15%
or 0.08λ peak-valley.

[0129]If we stay with α=0.92 per micron then we need 100 times
higher dose than the dose at the threshold as shown in FIG. 4. The
relative dose accuracy at the least dose need to be 5% i.e. the
background noise in the image has to be less than 1/100*5%=0.0005 of the
highest dose. Therefore we need a writing system with a signal to noise
of 2000:1. (The noise may come from internal reflections, non-perfect
extinction in the modulator, stray light, and inaccurate dose. Above all
the writing system needs to have high contrast so the presence of the
maximum dose in an area does not contaminate the clean exposure of the
lowest one. The grey-value bitmap representing the dose needs to have at
least as much dynamic range as the writing system, and in the examples
above a 12-bit representation may be suitable, corresponding to a signal
to noise of 4096:1, or in a different preferred embodiment of the present
disclosure at least 10 bits or 1024:1. Previously known optical writers
have 8-bit representations of the bitmap in optical writers and a signal
to noise typically below 256:1.

[0130]The example discussed above shows that the useable α depends
of the profile depth and in order to write a variety of different profile
depth it is useful to have a selection of resists with different α.
All resists have some level of absorption, and resists with added dyes to
make them more absorbing are known in the art, e.g. as a means to avoid
reflecting notching on metal layers with topology. According to preferred
embodiments of the present disclosure, the absorption in the resist used
for producing three-dimensional patterns on a workpiece can be made
higher by addition of a dye or pigment, e.g. soot. Red, green, blue, and
black resists made for LCD color filters can be used as a selection of
resists with different absorption coefficients at the writing wavelength.

Use of Multiple Focal Depths and Numerical Apertures

[0131]Another way to enhance the precision of latent image formation is to
expose the resist in N different passes with more than one focus settings
in τhe z-direction. Different focal plane positions from the top of
the resist through the resist layer can be applied to different exposure
passes. By defining M different focus settings, the negative effects of
the Gaussian-beam divergence can be reduced. Each of the relief depths
within one layer will then be exposed with approximately the same
Effective Spot Size. This is useful to improve the resolution both in the
lateral x-y-direction and in the vertical z-direction.

[0134]FIG. 15 adds to FIG. 14 a representation of varying pixel sizes in
different exposure phases. Each of the focal planes 1511, 1512, 1513 has
been given an individual grid size. A finer grid size 1513 is applied
where the relief features 1533 are sharpest. A fictive relief, with a
sharper tip deeper in the photoresist, is shown as a hatched line 1533. A
positive photoresist is assumed. The of exposing 1521, 1532, 1534. There
are a multitude of different possible methods to set the different focal
planes, and to match those to the desired exposure doses at all the
certain depths, for all the N exposures, in the resist. Examples of
possible exposure patterns embodiments are given below.

[0135]Selecting a Single Focal Plane

[0136]One approach is to use a simple linear interpolation between the N
layers. Following this approach, layers which in turn may contain several
exposure doses which will reach different depths in the resist after
development (assuming a positive photoresist), may be assumed to be
exposed with an "average focus".

where E is the 2.5D surface after exposure, I is the ideal 2.5D surface
that is the pattern, F is an vector with different focuses and N is a
vector with fixed different parameters that affect the exposure, for
example resist parameters, development time etc.

[0138]There are several ways to solve this equation above using commercial
software. One method is the Newton-Raphsons method; more generally,
methods of non-linear optimization can be applied. Recall from above that
the function E can be calculated as function of F. As a relatively crude
approximation, the E can be calculated using a convolution between the
object and some function that described the optical system (including or
not including the development process). This method of calculating E is
relatively fast and can be used for large patterns. Better, if the
pattern repeats or if resources permit, one or more unit cell could be
rigorously simulated using either commercial available or specially
developed software that simulates the exposure. For instance, a full
propagation model and a complex chemical model for the development and
process and circular boundary conditions could be applied.

[0139]When solving the equation above, one can effectively start with one
focus layer, derive a result, then repeat the process adding more focal
planes one at a time until the merit function does not improve more than
a certain limit. The maximum amount of focal planes can be set before the
analysis begins or could be selected based on results of the analysis.

[0140]Another approach is to approximate the exposure process of each of
the N exposures with a mathematical convolution of the exposing doses For
instance, once can apply a Gaussian "kernel" and an "average focus"
within each of the N exposures, for each of the depths that will be
reached in the resist after the development. Perform the calculations of
the N different 2-D convolutions, with the applicable Gaussian width and
peak value. Alter the outcome after comparison to the original relief,
and once again perform the N 2-D convolutions. Iterate until the process
converges.

[0141]Another approximation of the multi-focal exposures can be obtained
by applying 3-dimensional convolution to calculate the exposure doses of
each of the N individual exposures. That can be made by either
approximating the 3-dimensional convolution in the z-direction by
discrete summations of the contributions from the N discrete exposures,
or performing a 3-dimensional convolution using Volume pixel elements, or
Voxels, throughout the entire volume of the photo-sensitive material.

[0142]Multiple Focal Planes

[0143]When using high resolution optics in combination with a thick resist
you will face the problem that the spot radius will vary through the
resist. This will affect the resolution and you will get different
resolution at different Z-positions in the resist.

[0144]To improve fidelity over the full depth of the profile, use can be
made of a flexible, or adaptive, definition of (the N dose-boosting
layers, and) the M focus layers by a first analysis of where the
strongest gradients ∂z/∂x and
∂z/∂y are located in both the x- and
y-directions, and--more important--in the z-direction. That may be done
in a preparation software processing system. For relief "pattern" details
that have sharp z-direction details that produce high spatial frequencies
at deep levels in the photo-sensitive material, the corresponding focal
planes where those relief details appear should be positioned deep in the
material, preferably as deep as possible. For relief "pattern" details
which have sharp z-direction details that produce high spatial
frequencies at shallow levels in the photo-sensitive material, the
corresponding focal planes for those relief details should be positioned
shallow in the material, or even at the resist surface. For relief
"pattern" details that have sharp z-direction details at intermediate
levels in the photo-sensitive material, the corresponding focal planes
for those relief details should be positioned at intermediate depths. In
all cases, the depth positioning of relief levels within the different
focal planes is arranged by the exposure dose. In practice, this means
that the dose used to define the pattern is assigned to one of the focal
planes. Think of a pyramid with a sharp tip and a sharp angle where the
sides meet the ground or floor. The area around the tip is exposed in a
writing pass with focus near the tip, and the lower parts of the sides
are exposed in a pass with focus near the ground. Each pass is described
by a bitmap, and the low-focus bitmap contains only zeros around the tip,
so that the bitmap in the high-focus bitmap determine the shape of the
tip. For xy coordinates corresponding to the lower parts of the sides,
the high-focus contains zeros or small values and the surface shape is
determined by the data in the low-focus bitmap. In intermediate areas
both bitmaps have non-zero data and the exposure dose is divided between
the two passes.

[0145]If the pyramid is low compared to the focal depth, one pass with a
single focus setting may be enough. If, on the other hand, the pyramid is
high compared to the depth of focus two passes may not be enough to
define details on all levels, and more passes and focus levels may be
used. The dose at a specific xy point is then assigned to one or more
passes which give the best 3D fidelity to the data. To determine the
number of passes needed and how to assign the doses to the layers, i.e.
to determine the layer bitmaps, in the presence of complex patterns,
absorption, bleaching, defocus and developer kinetics is a non-trivial
task. We disclose for this purpose software algorithms and hardware to do
this automatically.

[0146]In other circumstances, the dose setting of the N exposures can be
incorporated into the non-linear exposure characteristics of the
photo-sensitive material, which in a 3-D application is shown by its
depth-vs-dose function. One of the root causes to the non-linearity of
the photoresist depth-vs-dose response is the so-called bleaching that
results from depletion of the photo-active compound (PAC) during the
absorption of the exposing radiation/electromagnetic
radiation/light/laser light. Compensating for non-linear effects and
bleaching effects is useful when setting doses in an N-exposure writing
scheme.

[0147]Impact of Thickness on Divergence

[0148]FIGS. 16 and 17A depict beam divergence patterns in resist layers
that are 1 and 80 μm thick, respectively. FIG. 17B is an enlargement
of a section of the 80 μm thick resist, which shows a section 5 μm
thick and makes it easier to visualized convergence and divergence
pattern in the thick resist. In FIGS. 16-17, the vertical axis is scaled
to match the resist thickness. Accordingly, the axes have much different
scaling factors. In each figure, the focal plan is set to the middle of
the resist layer. For the 1 μm thick resist in FIG. 16, exposure is in
a tight column, with relatively little divergence. For the 80 μm thick
resist, FIG. 17B is provided to improve comprehension of the convergence
and divergence pattern in the 80 μm thick resist. From this enlarged
simulation result, one can see a so-called waist in the focus that
extends about +/-300-400 nm on either side of the "0" position focal
plane. Within about +/-1.5 μm of the focal plane for the 80 μm
thick resist, the beam is workably narrow. The reported numerical
aperture of 0.55. In air, this would correspond to a half-angle of about
33 degrees or a focal cone of about 67 degrees. The resist is specified
as having an X2 response. The refractive index is not given in the
figures, but may have been about 1.5, which is less than 1.7, which is a
reasonable target value. Divergence produces rounding of some features in
a latent image.

[0149]A usefully precise measure of beam divergence and, therefore, of
depth of focus is the so-called Rayleigh range. Applying the Rayleigh
range zR as the criteria for the depth of focus, the Rayleigh range
extends a distance on either side of the focal plane for which the beam
cross-section is not larger than square root of two times the diameter of
the beam cross-section at the best focal plane. We use two times the
Rayleigh range distance as the depth of focus, as further explained
below.

[0150]The depth of focus can be defined in many ways. In practice, the
usable depth of focus is often determined empirically as the largest
focus latitude that is compatible with acceptable yield. This practical
approach depends on the design, performance specifications and economic
value of the structures produced.

[0151]For patent purposes and in this disclosure, we use the following
definition of the depth of focus DOF, as twice the Rayleigh range zR
for a beam which is Gaussian or approximately Gaussian. Mathematically,

DOF=2zR=2πw02/λ=2λ/(πNA2)

where w0 is the 1/e2 beam radius at the beam waist. It is
related to NA through

w0=2λ/(∂Θ)=λ/(πNA)

where NA is Sin(Θ/2) and Θ/2 is the angle from the center line
of a diverging beam where the intensity has fallen to 1/e2 of the
value at the center. λ is the wavelength in the medium, in this
case, the wavelength in the resist, which typically has a refractive
index of about 1.7 for UV wavelengths. The formula uses the paraxial
approximation where sin(Θ/2)=Θ/2. For some optical systems,
in particular image-projection systems using partially coherent
illumination, the definition DOF=λ/NA2 applies to fairly
approximate the depth of focus. The difference between
DOF=21λ/(λ/NA2) for a Gaussian beam and λ/NA2
for an imaging system comes partly from the different physics, partly
from the top hat vs. Gaussian filling of the NA with light.

[0152]For some purposes, it is useful to define thin and thick resist
using this Rayleigh range definition of depth of focus. We define thin
resist to have a vertical thickness of less than or equal to one or two
times the depth of focus. Thick resist has a vertical thickness of
greater than or equal to either four or five times the depth of focus. In
thin resist, convergence and divergence effects are relatively moderate.
In thick resist, convergence and divergence effects should, in the view
of these inventors, be taken into account explicitly. Either four or five
times the depth of focus can be chosen as a practical definition of when
a resist is considered thick for purposes of this disclosure. We will use
these definitions of thin and thick resist throughout this disclosure.

[0153]Impact of Focal Plane Choice on Pattern

[0154]FIG. 18 shows the difference between ideal and exposed in a 20 μm
resist layer, when the focal plane is set at 10 μm. The ideal feature
has vertical sides, like a semi-sphere. The resulting exposure has an
inflection point at about the focal plane, witching from a convex solid
to a converse solid. The differences graph of FIG. 18 dramatically
illustrates the formation of fillets where the feature sides are supposed
to be vertical.

[0155]The conventional patterns for lithography in 2D do not translate
well to 2.5D because 2D patterns are usually binary: the resist is either
exposed or not. Greyscale values are only used for the positioning of the
edge with subpixel accuracy. In 2.5D applications, each greyscale value
is mapped to a specific thickness after development of the photo resist.
Thus, the pattern for a 2.5D feature will contain much more grey scale
values than patterns used for 2D lithography.

[0156]Gradients to Select Focal Plane(s)

[0157]For thick resist, one or more focal planes are selected to best
reproduce the ideal feature in the thick resist layer. To select a single
focal lane for the semi-sphere, for instance, a computer can be used to
calculate gradients across the x and y grid, either from a pixelmap or
for a pattern described by mathematical functions. The computer then
calculates the normal vector either directly from the gradients or from a
filtered version, either from a linear filtered version or a non-linear
filtered version, of the gradients. Then for each z-height (the total
thickness will be divided into several subsections), a distribution of
the angles between the normal vector and XY-plane will be calculated.

[0158]By analyzing the distribution of the normal vector directions for
these z-heights, the computer can select or assist a user in selecting
focal planes at various z-heights that give a close match between the
ideal features and the exposed result. An optimization search for a focal
plane height can use linear or non-linear techniques. The penalty
function used can be a function of the focus-height, z-height, the normal
vector angle, or another measure.

[0159]FIG. 19 applies this algorithm to the semi-sphere pattern, depicting
gradients and the gradient distribution. The data in the lower graph of
FIG. 19 together with a distribution function for gradients at each
z-height can be used to select the correct focal plane. A simple
selection approach selects one focal plane. In the example above, the
selection ignore average gradients below the so-called relaxation limit
of 200. Depending on the geometry and desired sharpness of vertical
corners, the relaxation limit may be higher or lower. In the top graph of
FIG. 19, there is one pair so-called vertical corners, both at the same
z-height, where the flat horizontal runs abruptly turn upward at the
vertical edges of the semi-spheres. In the lower graph of FIG. 19, which
plots the absolute value of average gradients against vertical position
within the relief map or resist layer, the position of all vertical
corners at the same height produces one peak in the graph. The focal
plane is selected as depicted in FIG. 20. The relaxation limit, indicated
by the horizontal dotted line, is used to isolate the part of the pattern
in which the focal plane will be located. The position of the focal plane
is selected based on a centre of gravity of the area above the relaxation
limit. In FIG. 20, the area is a triangle and calculated focal plane
height is around 0.27 μm.

[0160]The selection of a number of focal planes used to cover a single
area above the relaxation limit will depend on the vertical extent being
exposed, as a ratio of the depth of focus. The greater the available
depth of focus, the greater the vertical extent of resist that can be
effectively exposed by a focus in a single focal plane. In FIG. 20, the
vertical extent of resist near the vertical corner and having a high
average gradient is indicated by the base of the triangle. When this base
is longer than some threshold factor of the depth of focus, multiple
exposures will be needed. The factor may be one or two, which corresponds
to our definition of a thin resist. When the depth of exposure exceeds
the threshold, the vertical extent is partitioned into two or more
vertical extents and focal planes are selected for the multiple vertical
extents. Alternatively, if the number of focal planes allowed for
exposing the resist layer is lower than the number of subsections, the
focal planes are distributed in order to minimize the sum of the least
squares norm (sometimes called the L2 norm) between each center of
gravity and the closest focal planes.

[0161]FIG. 22 depicts a more complicated 2.5D relief, with a pillar and
cap on top of an ellipse. Vertical corners are at about 0, 8 and 12
microns height. These corners are apparent in both the cross section in
the top of FIG. 22 and the average gradient peaks in the bottom of the
figure. Note the peak 2 and 3 is lower than the first one since the
average absolute value of the gradient is calculated within a height
interval and the sharp step only contains one sample point. The
relaxation limit has adaptively been set at 50, to capture all three
peaks. Preferably, three focal planes are selected. With three focal
planes available, the algorithm will here place the planes at 0.27 μm,
8.25 μm and 12.25 μm. If a fewer focus layers are allowed, the
algorithm may focus on the gradient peaks in the bottom graph of FIG. 22
that have highest Z-height components. For example if two focus layers
were allowed it would have been 0.27 μm and 8.25 μm in the case
above. Alternatively, if less than three are available, the sum of least
squares between centers of gravity and focal planes can be calculated to
position the focal planes. Or, where there are dominant peaks, as in FIG.
22, focal planes can be allocated to those peaks and the one of the least
squares approaches described above can be applied to position the
remaining peaks. This, of course, depends on having enough focal planes
available to cover the dominant peaks and the remaining vertical segments
that are outside the depth of focus of the focal planes selected to cover
the dominant peaks.

[0162]Several variants of the algorithm are readily available. On could,
for example, change the selection function to use maximum gradients in
areas, instead of average gradients. Or, one could use a function that is
based on higher moments than the gradient. The selection function can
also vary. For example, based on calculating a mean instead of centre of
gravity or matching focal planes to the gradient peaks.

[0163]With multiple focal planes, one should understand that doses are
distributed among the focal planes, with doses emphasized in any plane(s)
that contain a vertical corner. In FIG. 21, an x, y coordinate will have
only one vertical corner at one height in one focal plane. In FIG. 22,
some x, y coordinates have two vertical corners at different heights, so
the dose will be distributed between the focal planes closest to the top
and bottom of the pillar on top of the ellipse.

[0164]FIGS. 22-23 are photo micrographs of some features in resist that
were formed using differently positioned focal planes. FIG. 22 had its
focal plane selected by applying the approach described. FIG. 23, in
contrast, was exposed with a less well chosen focus setting. FIG. 22 has
sharper edges, as a result of the focal plane selection.

[0165]The method above can also be generalized by further allowing for
several focus layers. These focus layers can be written in one pass by
dynamically changing focus or using a writing engine that can write to
several focal depths simultaneously, e.g. a multibeam writer with
different focus for each beam or a SLM/DMD writer with a tilted focal
plane over the chip. Alternatively, the data can be divided into several
passes that are written separately with different focus settings.

[0166]If several focus settings are allowed, the basic optimization is the
same as above except for that the optimization restraints are changed to
allow multiple focus layers. The algorithm will then label each pixel to
a certain focus layer.

[0167]Pattern Decomposition

[0168]FIG. 24 illustrates how the algorithm may divide the pattern into
two layers with different focus.

[0169]FIG. 25 illustrates the result assuming that the pattern is already
defined. FIG. 26 shows a flow chart for the algorithm.

Some Particular Embodiments

[0170]The present invention may be practiced as a method or device adapted
to practice the method. The invention may be an article of manufacture
such as media impressed with logic to carry out computer-assisted
formulation of an exposure map for three-dimensional patterning of
resist.

[0171]Some Methods

[0172]The first method embodiment forms a three-dimensional latent image
with good depth and shape control in a resist layer 2673 applied over a
workpiece 2683. This method is particularly well adapted to a thin resist
layer 2673, such as resist layer that is thinner 2663 than the depth of
focus of exposing system used the pattern to resist, which is defined
above as twice a Rayleigh range 2676. It also may be applied to a
moderately thin resist layer that is no more than twice as thick as the
depth of focus of the exposing tool.

[0173]This method includes using a positive resist with an effective
absorption characteristic that produces a log-linear relationship 2651
between the exposing energy and the depth of exposure. This log-linear
relationship may otherwise be described as an exponential relationship,
which is the inverse a log-linear relationship. The equations for a
first-order approximation of the log-linear or exponential are given in
the disclosure above. By first-order approximation, we mean that a more
precise curve fit to calibration data can be achieved by adding
additional terms or by taking into account processes in addition to the
dominant absorbing process.

[0174]The method proceeds with converting a relief map that represents a
three-dimensional surface 2611 into point-by-point exposure doses 2691
calculated to reach an exposure threshold of the positive resist at a
plurality of controlled depths within the resist layer 2673. When the
exposure doses are calculated, the calculation takes into account the
log-linear relationship. An exposure map is produced. This exposure map
may be prepared ahead of patterning and persisted for later use, or it
may be as needed for patterning and consumed by a pattern generator close
to the time that is prepared. Preparing the exposure map in advance may
have the advantage of facilitating simulation and improvement.

[0175]This method optionally includes patterning the resist layer to form
a three-dimensional latent image using a pattern generator 2615-2635 that
varies effective exposure doses 2691 on a point-by-point basis using the
exposure map.

[0176]This method can be extended by developing the latent image and
producing a device using the developed latent image. The device may be
produced directly or by replication. Examples of devices produced from
3-D patterning of resist are given in the disclosure above. One immediate
example is a lenticular lens for three-dimensional viewing of an image.
Alternatively, it may represent the relief map to a precision of at least
11 binary bits and use the 11-bit precision to produce exposure doses.
Or, it may be calibrated to produce at least 1000 or 4000 dose steps
between minimum and maximum exposure doses.

[0177]The positive resist used in the foregoing method may be a bleachable
resist. By bleachable 2677, we mean including a component that absorbs
photons, is converted by the photons, and is substantially a less
absorptive after the conversion. This bleachable component may be
essentially opaque prior to bleaching and transparent or translucent
after bleaching. This component may make the resist layer opaque, before
bleaching.

[0178]The effective absorbed a characteristic of the positive resist may
result from passive absorption 2678. That is, the positive resist may
include an effective quantity of a passive absorbing component that
absorbs photons without chemically exposing the resist, for instance,
converting the photons to heat. An effective amount of passive and
absorbing components may be used to cause a log-linear relationship 2651
between exposure energy and depth of the exposure. Two examples of
passive absorbing components are dye and nano-particles, such as soot.

[0179]When a log-linear relationship 2651 is present, the lower half of
the resist (below 2675), further away from the surface that is exposed
than the upper half of the resist (above 2675), requires more marginal
energy to expose then the upper half. If the upper half uses one unit of
energy, the lower half may use 2, 3, 4, 5 or more times as much energy as
the upper half Any of these proportions such as at least 3, may hold.
When the lower half requires twice the "one unit" of exposing energy as
the upper half, the total energy required to expose both halves will be
three units. Of course, reference to units in this context is reference
to arbitrary units. Alternatively, the lower quarter of the resist
requires 100 times as much marginal exposure energy as the upper quarter.

[0180]The positive resist used in this method may have a gamma of five or
greater (FIG. 2a). Alternatively, the resist may have a gamma of 8 or
greater.

[0181]The pattern generator used may be a laser pattern generator
2615-2635.

[0182]A second method embodiment forms a three-dimensional latent image
with good depth and shape control in a thick resist layer applied over a
workpiece 2683. A thick resist layer may be 1.5 times as thick 2763 as
the depth of focus of the pattern generator used to expose the resist,
where the depth of focus is twice a Rayleigh range 2776. Alternatively, a
thick resist layer may be twice as thick 2763 as the depth of focus. As
illustrated in the figures, a thick resist alternatively may be at least
three times as deep as the depth of focus.

[0183]This method proceeds using a thick positive resist that has a gamma
of five or greater (FIG. 2a). Alternatively, the resist may have a gamma
of 8 or greater. A gamma value corresponds to the steepness of exposure
to dissolution rate curve, as illustrated in the figures. The higher the
gamma, the narrower the dose band that moves the resist from having a
very low dissolution rate to having a very high dissolution rate. A high
gamma resist is also said to be a high contrast resist. It is suitable
for endpoint or essentially endpoint processing. By essentially endpoint,
we mean that the resist is dissolved until the rate of dissolution has
dropped off very substantially, so that the development and dissolution
process is relatively insensitive to the development time allowed. In
contrast, the low gamma resist is often uses a carefully timed the
etching process, giving a relief depth that is proportional to the
etching time. A timed process, of course, is sensitive to etching time
and other development-related factors.

[0184]The value of gamma is a function of the type of resist chemistry,
the resist concentration of the PAC, the baking time and temperature, and
the developer. The dissolution is very slow up to a threshold value, and
grows approximately linearly for high doses. The high contrast is
achieved at the knee between very low dissolution rate and a dissolution
rate which grows fast with the exposure dose. Therefore, the gamma value
is high when development is slow and fast development means moving up on
the linear part of the dissolution curve, giving low contrast and gamma.
The gamma is therefore as much a property of the process, as of the
resist material, and it is known that cold diluted developer produces
very high gamma in some resist formulations. On the other hand, published
dissolution curves in descriptions of laser- and ebeam processes for 3D
(or 2.5D) surfaces often shows an approximately linear relation between
remaining thickness and dissolution rate, i.e. a gamma around 1.

[0185]This second method proceeds with converting a relief map that
represents a three-dimensional surface 2611 into point-by-point exposure
doses calculated to exceed an exposure threshold of the positive resist
at a plurality of controlled depths within the resist layer. The
calculation optionally takes into account the numerical aperture 2656 of
the exposing system. The numerical aperture value can be taken into
account analytically or by empirical observation of in exposure of resist
using different numerical apertures. The converted relief map results in
exposure map will, as described above.

[0186]This method optionally proceeds with patterning the resist layer in
multiple writing passes to form a three-dimensional latent image. The
patterning uses a high dynamic range pattern generator 2615-2635 that
varies exposure doses on a point-by-point basis using the exposure map
2691. By high dynamic range, mean a pattern generator calibrated produce
at least 1000 steps between minimum and maximum exposure doses. It may
use 11 binary bits or more precision. Alternatively, the pattern
generator may be calibrated to produce at least 4,000 steps between
minimum and maximum exposure doses.

[0187]The positive resist used in the foregoing method may be a bleachable
resist. By bleachable 2677, we mean including a component that absorbs
photons, is converted by the photons, and is substantially a less
absorptive after the conversion. This bleachable component may be
essentially opaque prior to bleaching and transparent or translucent
after bleaching. This component may make the resist layer opaque, before
bleaching.

[0188]The resist may have a passive absorption characteristic. That is,
the positive resist may include an effective quantity of a passive
absorbing component that absorbs photons 2678 without chemically exposing
the resist, for instance, converting the photons to heat. An effective
amount of passive and absorbing components may be used to cause a
log-linear relationship between exposure energy and depth of the exposure
2651. Two examples of passive absorbing components are dye and
nano-particles, such as soot.

[0189]The pattern generator 2615-2635 used may be a laser pattern
generator.

[0190]Aspects of the first and second methods can be interchanged or
recombined, as typically expressed in a dependent claim that depends from
any of the forgoing claims. They also may be combined with features
described in the foregoing disclosure.

[0191]A third method forms a three-dimensional latent image with good
depth and shape control in a thick resist layer 2863 applied over a
workpiece 2883. The meaning of thick resist in this method is as above.
Of course, aspects of the first and second methods can be interchanged
and recombined with aspects of the third method, as above.

[0192]The third method proceeds using a positive resist. It includes
selecting multiple focal planes 1511, 1512, 1513 at which to focus
exposing energy. At least one of focal planes 1513 is in a lower half of
the resist layer. By lower half, we mean the half of the resist that is
further from a surface to which exposing energy 2855 is applied than the
upper half.

[0193]This method continues with converting a relief map that represents a
three-dimensional surface into point-by-point and layer-by-layer and
exposure doses 2691 calculated to exceed an exposure threshold of the
positive resist at a plurality of controlled depths within the resist
layer. The calculation takes into account the numerical aperture value
2656 to be used during patterning. Different numerical apertures may be
applied to different focal planes. Applicable numerical apertures may be
automatically selected. The method produces an exposure map 2691.

[0194]This method optionally proceeds with patterning the resist layer
using the multiple focal planes to form a three-dimensional latent image,
using a pattern generator 2615-2635 that varies effective exposure doses
on a point-by-point basis using the exposure map 2691.

[0195]Another optional aspect of this method is selection of the focal
plane 1513 in the lower half of the resist layer (below 2675) to
emphasize accurate patterning of vertical or near-vertical aspects of
features (e.g., 501, 1911) in the relief map. By vertical, we mean
perpendicular to the surface of the workpiece 2883. Multiple focal planes
can be automatically selected by identifying two or more vertical corners
2111, 2113, 2115 in features in the relief map that are at different
vertical heights within the relief map and selecting two or more focal
planes 1511, 1513, 1515 corresponding to the two or more corners and
positioning them to enhance the three dimensional latent image of the
vertical corners.

[0196]Alternatively, the focal plane in the lower half of the resist may
be selected to emphasize accurate patterning of features in the relief
map that have sharp z-direction details 1533. Or, the focal plane in the
lower half may be selected to emphasize accurate patterning of features
in the relief map that have relatively high spatial frequencies, as
compared to other features in the relief map.

[0197]As in the second method, the pattern generator 2615-1635 used in the
third matter used in the third method may have a high dynamic range. That
is, it may be calibrated to produce at least 1000 dose steps between
minimum and maximum exposure doses, to use at least 11 bits precision, or
to produce at least 4000 dose steps.

[0198]Optionally, pixels of different sizes (FIG. 15) can be used in the
multiple focal planes 1511, 1513, 1515.

[0199]Exposure in the different focal plans may be accomplished in a
single writing pass by a pattern generator that supplies multiple beams
2855 that are focused in the different focal planes (FIG. 28). The
pattern generator may expose the multiple focal planes in multiple
writing passes 2832.

[0200]Exposure doses are allocated among layers 1511, 1513, 1515 and
stored in the exposure map 2691 on a layer-by-layer basis. There are a
variety of alternative ways of allocating exposure doses among the focal
planes.

[0201]As described above, the allocation of doses among layers may involve
applying linear interpolation, or 2D convolutions applied at depths
selected from the relief map, or 3D convolutions simulating writing
exposures in the multiple focal planes. The simulation may involve fully
3D convolutions, using volume pixel elements, also known as voxels.

[0202]This method may automatically select and/or position focal planes
1511, 1513, 1515. It may select one focal plane or two or more focal
planes. It may automatically position any number of focal planes, whether
selected automatically or by an operator.

[0203]The pattern generator 2615-2635 may be a laser pattern generator.

[0204]A fourth method forms of a three-dimensional latent image with good
depth and shape control in a layer of resist 2673, 2773 applied over a
workpiece 2683, 2783. It involves two or more iterations 2903 to improve
an exposure map 2901. The method proceeds with converting a relief map
that represents a three-dimensional surface 2611 into point-by-point
exposure doses 2901. The point-by-point exposure doses are calculated to
exceed an exposure threshold of the resist at a plurality of controlled
depths within the resist layer, producing an exposure map.

[0205]The method proceeds with two or more iterations 2903 of simulating
on a computer 2902 the patterning of the resist layer with a pattern
generator that varies effective exposure doses on a point-by-point basis
using the exposure map. This simulating produces a simulated
three-dimensional latent image 2925, 2926. The simulated
three-dimensional latent image 2925, 2926 is compared 2924 to the relief
map 2611. The exposure map is revised using results of the comparing.

[0206]This method may iterate 2903 five or ten times or more.

[0207]A further aspect of this method involves calculating a sweep
adjustment during the converting of the relief map. A sweep adjustment
takes into account a direction of travel of exposing radiation across the
resist layer and compensates for non-linear effects related to whether
the exposure is building or diminishing (FIG. 5) as the exposing
radiation moves across the resist layer. The calculated sweep adjustment
may be incorporated into the exposure map.

[0208]This method also may include the simulating step taking into account
the direction of travel of exposing radiation (FIG. 5) across the resist
layer and non-linear effects related to whether exposure is building or
diminishing as the exposing radiation moves across resist layer.

[0209]The resist used in the foregoing method may be a positive,
bleachable 2677 resist. By bleachable, we mean including a component that
absorbs photons, is converted by the photons, and is substantially a less
absorptive after the conversion. This bleachable component may be
essentially opaque prior to bleaching and transparent or translucent
after bleaching. This component may make the resist layer opaque, before
bleaching.

[0210]The resist may have a passive absorption characteristic. That is,
the positive resist may include an effective quantity of a passive
absorbing component 2678 that absorbs photons without chemically exposing
the resist, for instance, converting the photons to heat. An effective
amount of passive and absorbing components may be used to cause a
log-linear relationship 2651 between exposure energy and depth of the
exposure. Two examples of passive absorbing components are dye and
nano-particles, such as soot.

[0211]This iterative method may be applied to refine any of the foregoing
methods of forming a three-dimensional latent image. In a thick layer of
resist, this method may be extended by defining multiple focal planes
1511, 1513, 1515 at which to focus exposing energy. The relief map may be
converted into point-by-point and layer-by-layer exposure doses,
producing the exposure map 2691, 2901. The simulation, in turn, proceeds
taking into account the multiple focal planes.

[0212]The meaning of a thick layer in this extension of the fourth method
is as described above. The positive resist the simulated may have a gamma
of five or greater or, alternatively, eight or greater. This simulating
may take into account the numerical aperture 2656 of the pattern
generator 2615-2635 when writing to the multiple focal planes. The
simulated pattern generator and may be a high dynamic range pattern
generator that is calibrated to produce a least 1000 dose steps between
minimum and maximum exposure doses, or that is calibrated to produce at
least 4000 dose steps.

[0213]The iteration may be continued beyond one refinement, repeating the
simulating, comparing and revising actions until results of comparing the
difference 2924 between successive simulated three-dimensional latent
images 2925, 2926 satisfies a predetermined criterion.

[0214]In a thick resist layer, the method may further include defining
multiple focal planes 1511, 1513, 1515 at which to focus exposing energy
2655, 2855, converting the relief map into point-by-point and
layer-by-layer exposure doses 2691, the exposure doses allocated by
layer, producing the exposure map 2901, and simulating the patterning of
the resist layer 2925, 2926 using the multiple focal planes.

[0215]Focal plane positions and/or counts may be automatically selected
based on data in the relief map, such as data that describes vertical
corners.

[0216]A thick layer may be as described above, 1.5 or two or three or more
times the depth of focus of a pattern generator.

[0217]The resist may have a gamma of 5 or 8 or greater.

[0218]The simulating may take into account a numerical aperture 2656 of
the pattern generator 2615-2635, which may change from one focal plane to
the next or one writing pass to the next.

[0219]The simulated pattern generator may be configured to produce at
least 1000 dose steps, or to use at least 11 binary bits precision or to
produce at least 4000 dose steps.

[0220]This method optionally includes using a pattern generator, such as a
laser pattern generator, to apply the refined exposure map to patterning
a thin or thick layer of resist applied to the surface of a workpiece. As
previously mentioned, the method may be extended by developing the resist
and producing devices using the developed resist.

[0221]The pattern generator may be a laser pattern generator.

[0222]Devices that Practice the Methods

[0223]Each of the methods described above involve close cooperation among
specialized hardware components. Maps are stored in memory. Map
processors are used to convert maps and apply transfer functions.
Simulation processors are used to conduct simulations. Lasers, lenses and
resist are used to form latent images on workpieces. The lasers and
resists have a variety of alternative characteristics, as described
above. Depending on the application, the map and simulation processors
may determine point-by-point exposures for different thicknesses and
characters of resist.

[0224]Articles of Manufacture

[0225]While the present invention is disclosed by reference to the
preferred embodiments and examples detailed above, it is understood that
these examples are intended in an illustrative rather than in a limiting
sense. Computer-assisted processing is implicated in the described
embodiments. Accordingly, the technology disclosed may be embodied in
methods for calculating exposure doses and writing passes to create 2.5D
latent images in resist with a high gamma. It may be embodied in systems
including logic and hardware resources to calculate exposure doses and
writing passes, systems that take advantage of computer-assisted
calculation of exposure doses and writing passes, computer readable
storage media impressed with logic to carry out calculation of exposure
doses and writing passes, data streams impressed with logic to carry out
calculation of exposure doses and writing passes, or computer-accessible
services that carry out computer-assisted calculation of explore doses
and writing passes. It is contemplated that modifications and
combinations will readily occur to those skilled in the art, which
modifications and combinations will be within the spirit of the invention
and the scope of the following claims.

[0226]The methods, devices and articles of manufacture can be combined
with or applied using a writing system as described, thereby creating a
2.5D latent image in the resist layer. The 2.5D latent image can be
developed to produce a 2.5D structure. The 2.5D structure might be used
directly or may be used as masters for replication and production of
micro-structures, as generally described above. The resulting structures
may be optical, mechanical, fluidic or similar component or devices.